A mounting apparatus of this kind is disclosed in DE 42 29 089. Therein, on the front and back ends of a bridge-shaped bracket are respectively deployed, as bracket elements: on one side, a fixed clamp, and on the opposite side, an adjustable clamp. The adjustable clamp is implemented as a single unit with an operating element implemented as a swing arm, and connected to the bracket via a threaded connection. The mounting apparatus is fitted to a handgun in such a way that only the fixed clamp can be engaged with the corresponding blind holes in the handgun. Subsequently, the clamp is rotated via the swing arm from a release position to a clamping position. Due to the threaded connection, the clamp thus moves along with the shaped swing arm in the direction of the handgun, and comes into contact with the corresponding cut-outs of the handgun. By a further rotation of the clamp, the apparatus is locked to the handgun. Wear and tear or signs of use may occur due to frictional wear, especially in the case of delicate surfaces, due to the rotation of the clamp across the cutouts of the handgun that occurs during fastening.